Improved Image Classification with Manifold Neural Networks

TL;DR

This paper explores the use of Graph Neural Networks on image data by constructing an image manifold with variational autoencoders, enabling effective classification and demonstrating GNNs' potential beyond traditional graph data.

Contribution

It introduces a novel approach to applying GNNs to image data through manifold construction, bridging the gap between graph learning and image classification.

Findings

GNNs achieve competitive accuracy on MNIST and CIFAR10.

GNNs generalize well to unseen graphs in image classification.

Manifold-based graph construction preserves geometric information.

Abstract

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting from GNNs' message-passing framework. However, the potential of GNNs in more general data representations, especially in the image domain, remains underexplored. Leveraging the manifold hypothesis, which posits that high-dimensional data lies in a low-dimensional manifold, we explore GNNs' potential in this context. We construct an image manifold using variational autoencoders, then sample the manifold to generate graphs where each node is an image. This approach reduces data dimensionality while preserving geometric information. We then train a GNN to predict node labels corresponding to the image labels in the classification task, and leverage convergence of GNNs to manifold neural networks to analyze GNN generalization. Experiments on MNIST and CIFAR10 datasets demonstrate that GNNs generalize effectively to unseen graphs, achieving competitive accuracy in classification tasks.